Simplify the following expression: $a = \dfrac{k^2 + 15k + 54}{k + 9} $
Solution: First factor the polynomial in the numerator. $ k^2 + 15k + 54 = (k + 9)(k + 6) $ So we can rewrite the expression as: $a = \dfrac{(k + 9)(k + 6)}{k + 9} $ We can divide the numerator and denominator by $(k + 9)$ on condition that $k \neq -9$ Therefore $a = k + 6; k \neq -9$